A government researcher is analyzing the relationship between retail sales (in $ millions) and the gross national product (GNP in $ billions). He also wonders whether there are significant differences in retail sales related to the quarters of the year. He collects 10 years of quarterly data. A portion is shown in the accompanying table. 

a. Estimate y = β₀ + β₁x + β₂d₁ + β₃d₂ + β₄d₃ + ɛ, where y and x represent retail sales and GNP, respectively; d₁ equals 1 if quarter 1, 0 otherwise; d₂ equals 1 if quarter 2, 0 otherwise; and d₃ equals 1 if quarter 3, 0 otherwise. Note that the reference category is quarter 4. 

b. Predict retail sales in quarters 2 and 4 if GNP equals $16,000 billion. 

c. Which of the quarterly sales are significantly different from those of the 4th quarter at the 5% level? 

d. Reformulate the model to determine, at the 5% significance level, if sales differ between quarter 2 and quarter 3. Your model must account for all quarters.

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Year Quarter 2007 2007 B 2016 1 2 ⠀ 4 Sales 921266 1013371 ⠀ 1299699 GNP 14301.854 14512.945 B 19134.463